The homotopy analysis method for q-difference equations

AbstractThe q-difference equations are kind of important problems in q-calculus and applied mathematics. In this paper, the homotopy analysis method is extended to find approximate solution for some of q-differential equations. The q-diffusion equation and some examples are analytically investigated. The series solutions obtained by the proposed method are checked by reducing the solutions of q-calculus problems to h-calculus approximate solutions when q→1

On the first order operators in bimodules

We analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.Comment: 13 pages, AMSLaTe

The SO(N) principal chiral field on a half-line

We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states.Comment: 7 pages, Late

High Time for Conservation: Adding the Environment to the Debate on Marijuana Liberalization

The liberalization of marijuana policies, including the legalization of medical and recreational marijuana, is sweeping the United States and other countries. Marijuana cultivation can have significant negative collateral effects on the environment that are often unknown or overlooked. Focusing on the state of California, where by some estimates 60% -- 70% of the marijuana consumed in the United States is grown, we argue that (a) the environmental harm caused by marijuana cultivation merits a direct policy response, (b) current approaches to governing the environmental effects are inadequate, and (c) neglecting discussion of the environmental impacts of cultivation when shaping future marijuana use and possession policies represents a missed opportunity to reduce, regulate, and mitigate environmental harm

Solutions of multigravity theories and discretized brane worlds

We determine solutions to 5D Einstein gravity with a discrete fifth dimension. The properties of the solutions depend on the discretization scheme we use and some of them have no continuum counterpart. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall-Sundrum type metric with a negative tension brane. However, no brane source is required. We show that this result is robust under changes in the discretization scheme. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We find however one particular scheme which leads to an undetermined lapse reflecting the reparametrization invariance of the continuum theory. We also find other solutions, with no continuum counterpart with changes in the metric signature or avoidance of singularity. We show that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales. We also discuss some cosmological solutions.Comment: 19 page

How to obtain a covariant Breit type equation from relativistic Constraint Theory

It is shown that, by an appropriate modification of the structure of the interaction potential, the Breit equation can be incorporated into a set of two compatible manifestly covariant wave equations, derived from the general rules of Constraint Theory. The complementary equation to the covariant Breit type equation determines the evolution law in the relative time variable. The interaction potential can be systematically calculated in perturbation theory from Feynman diagrams. The normalization condition of the Breit wave function is determined. The wave equation is reduced, for general classes of potential, to a single Pauli-Schr\"odinger type equation. As an application of the covariant Breit type equation, we exhibit massless pseudoscalar bound state solutions, corresponding to a particular class of confining potentials.Comment: 20 pages, Late

The Hanabi Challenge: A New Frontier for AI Research

From the early days of computing, games have been important testbeds for studying how well machines can do sophisticated decision making. In recent years, machine learning has made dramatic advances with artificial agents reaching superhuman performance in challenge domains like Go, Atari, and some variants of poker. As with their predecessors of chess, checkers, and backgammon, these game domains have driven research by providing sophisticated yet well-defined challenges for artificial intelligence practitioners. We continue this tradition by proposing the game of Hanabi as a new challenge domain with novel problems that arise from its combination of purely cooperative gameplay with two to five players and imperfect information. In particular, we argue that Hanabi elevates reasoning about the beliefs and intentions of other agents to the foreground. We believe developing novel techniques for such theory of mind reasoning will not only be crucial for success in Hanabi, but also in broader collaborative efforts, especially those with human partners. To facilitate future research, we introduce the open-source Hanabi Learning Environment, propose an experimental framework for the research community to evaluate algorithmic advances, and assess the performance of current state-of-the-art techniques.Comment: 32 pages, 5 figures, In Press (Artificial Intelligence

Group theoretical approach to quantum fields in de Sitter space I. The principal series

Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an operator subject to covariant transformations under the dS isometry group. This insures that it obeys canonical commutation relations, up to an overall factor which should not vanish as it fixes the value of hbar. However, contrary to what is obtained for the Poincare group, the covariance condition leaves an arbitrariness in the definition of the field. This arbitrariness allows to recover the amplitudes governing spontaneous pair creation processes, as well as the class of alpha vacua obtained in the usual field theoretical approach. The two approaches can be formally related by introducing a squeezing operator which acts on the state in the field theoretical description and on the operator in the present treatment. The choice of the different dS invariant schemes (different alpha vacua) is here posed in very simple terms: it is related to a first order differential equation which is singular on the horizon and whose general solution is therefore characterized by the amplitude on either side of the horizon. Our algebraic approach offers a new method to define quantum field theory on some deformations of dS space.Comment: 35 pages, 2 figures ; Corrected typo, Changed referenc